Complex division, imag part

Percentage Accurate: 62.4% → 96.5%

Time: 14.1s

Alternatives: 17

Speedup: 1.8×

Specification

Math

\[\begin{array}{l} \\ \frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))

C

double code(double a, double b, double c, double d) {
	return ((b * c) - (a * d)) / ((c * c) + (d * d));
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = ((b * c) - (a * d)) / ((c * c) + (d * d))
end function

Java

public static double code(double a, double b, double c, double d) {
	return ((b * c) - (a * d)) / ((c * c) + (d * d));
}

Python

def code(a, b, c, d):
	return ((b * c) - (a * d)) / ((c * c) + (d * d))

Julia

function code(a, b, c, d)
	return Float64(Float64(Float64(b * c) - Float64(a * d)) / Float64(Float64(c * c) + Float64(d * d)))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = ((b * c) - (a * d)) / ((c * c) + (d * d));
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{b \cdot c - a \cdot d}{c \cdot c + d \cdot d} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))

C

double code(double a, double b, double c, double d) {
	return ((b * c) - (a * d)) / ((c * c) + (d * d));
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = ((b * c) - (a * d)) / ((c * c) + (d * d))
end function

Java

public static double code(double a, double b, double c, double d) {
	return ((b * c) - (a * d)) / ((c * c) + (d * d));
}

Python

def code(a, b, c, d):
	return ((b * c) - (a * d)) / ((c * c) + (d * d))

Julia

function code(a, b, c, d)
	return Float64(Float64(Float64(b * c) - Float64(a * d)) / Float64(Float64(c * c) + Float64(d * d)))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = ((b * c) - (a * d)) / ((c * c) + (d * d));
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(N[(b * c), $MachinePrecision] - N[(a * d), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \frac{b}{\mathsf{hypot}\left(c, d\right) \cdot \left(\mathsf{hypot}\left(c, d\right) \cdot \frac{1}{c}\right)} - \frac{d \cdot \frac{a}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (-
  (/ b (* (hypot c d) (* (hypot c d) (/ 1.0 c))))
  (/ (* d (/ a (hypot c d))) (hypot c d))))

C

double code(double a, double b, double c, double d) {
	return (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - ((d * (a / hypot(c, d))) / hypot(c, d));
}

Java

public static double code(double a, double b, double c, double d) {
	return (b / (Math.hypot(c, d) * (Math.hypot(c, d) * (1.0 / c)))) - ((d * (a / Math.hypot(c, d))) / Math.hypot(c, d));
}

Python

def code(a, b, c, d):
	return (b / (math.hypot(c, d) * (math.hypot(c, d) * (1.0 / c)))) - ((d * (a / math.hypot(c, d))) / math.hypot(c, d))

Julia

function code(a, b, c, d)
	return Float64(Float64(b / Float64(hypot(c, d) * Float64(hypot(c, d) * Float64(1.0 / c)))) - Float64(Float64(d * Float64(a / hypot(c, d))) / hypot(c, d)))
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - ((d * (a / hypot(c, d))) / hypot(c, d));
end

Wolfram

code[a_, b_, c_, d_] := N[(N[(b / N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(d * N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 85.3% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{if}\;d \leq -6.4 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{b}{d}}{\frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -3.5 \cdot 10^{-102}:\\ \;\;\;\;\frac{b}{\frac{{\left(\mathsf{hypot}\left(c, d\right)\right)}^{2}}{c}} - d \cdot \frac{t_0}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;d \leq 2.5 \cdot 10^{-59}:\\ \;\;\;\;\frac{b}{c} - \frac{\frac{d \cdot a}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\mathsf{hypot}\left(c, d\right) \cdot \left(\mathsf{hypot}\left(c, d\right) \cdot \frac{1}{c}\right)} - t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ a (hypot c d))))
   (if (<= d -6.4e+146)
     (- (/ (/ b d) (/ d c)) (/ a d))
     (if (<= d -3.5e-102)
       (- (/ b (/ (pow (hypot c d) 2.0) c)) (* d (/ t_0 (hypot c d))))
       (if (<= d 2.5e-59)
         (- (/ b c) (/ (/ (* d a) (hypot c d)) (hypot c d)))
         (- (/ b (* (hypot c d) (* (hypot c d) (/ 1.0 c)))) t_0))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = a / hypot(c, d);
	double tmp;
	if (d <= -6.4e+146) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -3.5e-102) {
		tmp = (b / (pow(hypot(c, d), 2.0) / c)) - (d * (t_0 / hypot(c, d)));
	} else if (d <= 2.5e-59) {
		tmp = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	} else {
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - t_0;
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = a / Math.hypot(c, d);
	double tmp;
	if (d <= -6.4e+146) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -3.5e-102) {
		tmp = (b / (Math.pow(Math.hypot(c, d), 2.0) / c)) - (d * (t_0 / Math.hypot(c, d)));
	} else if (d <= 2.5e-59) {
		tmp = (b / c) - (((d * a) / Math.hypot(c, d)) / Math.hypot(c, d));
	} else {
		tmp = (b / (Math.hypot(c, d) * (Math.hypot(c, d) * (1.0 / c)))) - t_0;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = a / math.hypot(c, d)
	tmp = 0
	if d <= -6.4e+146:
		tmp = ((b / d) / (d / c)) - (a / d)
	elif d <= -3.5e-102:
		tmp = (b / (math.pow(math.hypot(c, d), 2.0) / c)) - (d * (t_0 / math.hypot(c, d)))
	elif d <= 2.5e-59:
		tmp = (b / c) - (((d * a) / math.hypot(c, d)) / math.hypot(c, d))
	else:
		tmp = (b / (math.hypot(c, d) * (math.hypot(c, d) * (1.0 / c)))) - t_0
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(a / hypot(c, d))
	tmp = 0.0
	if (d <= -6.4e+146)
		tmp = Float64(Float64(Float64(b / d) / Float64(d / c)) - Float64(a / d));
	elseif (d <= -3.5e-102)
		tmp = Float64(Float64(b / Float64((hypot(c, d) ^ 2.0) / c)) - Float64(d * Float64(t_0 / hypot(c, d))));
	elseif (d <= 2.5e-59)
		tmp = Float64(Float64(b / c) - Float64(Float64(Float64(d * a) / hypot(c, d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(b / Float64(hypot(c, d) * Float64(hypot(c, d) * Float64(1.0 / c)))) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = a / hypot(c, d);
	tmp = 0.0;
	if (d <= -6.4e+146)
		tmp = ((b / d) / (d / c)) - (a / d);
	elseif (d <= -3.5e-102)
		tmp = (b / ((hypot(c, d) ^ 2.0) / c)) - (d * (t_0 / hypot(c, d)));
	elseif (d <= 2.5e-59)
		tmp = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	else
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -6.4e+146], N[(N[(N[(b / d), $MachinePrecision] / N[(d / c), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -3.5e-102], N[(N[(b / N[(N[Power[N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision], 2.0], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] - N[(d * N[(t$95$0 / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 2.5e-59], N[(N[(b / c), $MachinePrecision] - N[(N[(N[(d * a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 84.5% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\frac{d \cdot a}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{if}\;d \leq -1.15 \cdot 10^{+167}:\\ \;\;\;\;\frac{\frac{b}{d}}{\frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -3.8 \cdot 10^{-111}:\\ \;\;\;\;\frac{b}{\frac{{\left(\mathsf{hypot}\left(c, d\right)\right)}^{2}}{c}} - t_0\\ \mathbf{elif}\;d \leq 1.36 \cdot 10^{-53}:\\ \;\;\;\;\frac{b}{c} - t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\mathsf{hypot}\left(c, d\right) \cdot \left(\mathsf{hypot}\left(c, d\right) \cdot \frac{1}{c}\right)} - \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (/ (* d a) (hypot c d)) (hypot c d))))
   (if (<= d -1.15e+167)
     (- (/ (/ b d) (/ d c)) (/ a d))
     (if (<= d -3.8e-111)
       (- (/ b (/ (pow (hypot c d) 2.0) c)) t_0)
       (if (<= d 1.36e-53)
         (- (/ b c) t_0)
         (-
          (/ b (* (hypot c d) (* (hypot c d) (/ 1.0 c))))
          (/ a (hypot c d))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((d * a) / hypot(c, d)) / hypot(c, d);
	double tmp;
	if (d <= -1.15e+167) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -3.8e-111) {
		tmp = (b / (pow(hypot(c, d), 2.0) / c)) - t_0;
	} else if (d <= 1.36e-53) {
		tmp = (b / c) - t_0;
	} else {
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - (a / hypot(c, d));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((d * a) / Math.hypot(c, d)) / Math.hypot(c, d);
	double tmp;
	if (d <= -1.15e+167) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -3.8e-111) {
		tmp = (b / (Math.pow(Math.hypot(c, d), 2.0) / c)) - t_0;
	} else if (d <= 1.36e-53) {
		tmp = (b / c) - t_0;
	} else {
		tmp = (b / (Math.hypot(c, d) * (Math.hypot(c, d) * (1.0 / c)))) - (a / Math.hypot(c, d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((d * a) / math.hypot(c, d)) / math.hypot(c, d)
	tmp = 0
	if d <= -1.15e+167:
		tmp = ((b / d) / (d / c)) - (a / d)
	elif d <= -3.8e-111:
		tmp = (b / (math.pow(math.hypot(c, d), 2.0) / c)) - t_0
	elif d <= 1.36e-53:
		tmp = (b / c) - t_0
	else:
		tmp = (b / (math.hypot(c, d) * (math.hypot(c, d) * (1.0 / c)))) - (a / math.hypot(c, d))
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(d * a) / hypot(c, d)) / hypot(c, d))
	tmp = 0.0
	if (d <= -1.15e+167)
		tmp = Float64(Float64(Float64(b / d) / Float64(d / c)) - Float64(a / d));
	elseif (d <= -3.8e-111)
		tmp = Float64(Float64(b / Float64((hypot(c, d) ^ 2.0) / c)) - t_0);
	elseif (d <= 1.36e-53)
		tmp = Float64(Float64(b / c) - t_0);
	else
		tmp = Float64(Float64(b / Float64(hypot(c, d) * Float64(hypot(c, d) * Float64(1.0 / c)))) - Float64(a / hypot(c, d)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((d * a) / hypot(c, d)) / hypot(c, d);
	tmp = 0.0;
	if (d <= -1.15e+167)
		tmp = ((b / d) / (d / c)) - (a / d);
	elseif (d <= -3.8e-111)
		tmp = (b / ((hypot(c, d) ^ 2.0) / c)) - t_0;
	elseif (d <= 1.36e-53)
		tmp = (b / c) - t_0;
	else
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - (a / hypot(c, d));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(d * a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.15e+167], N[(N[(N[(b / d), $MachinePrecision] / N[(d / c), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -3.8e-111], N[(N[(b / N[(N[Power[N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision], 2.0], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[d, 1.36e-53], N[(N[(b / c), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(b / N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 84.7% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.48 \cdot 10^{+141}:\\ \;\;\;\;\frac{\frac{b}{d}}{\frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -1.15 \cdot 10^{-105}:\\ \;\;\;\;\frac{b}{\frac{{\left(\mathsf{hypot}\left(c, d\right)\right)}^{2}}{c}} - d \cdot \left(a \cdot {\left(\mathsf{hypot}\left(c, d\right)\right)}^{-2}\right)\\ \mathbf{elif}\;d \leq 1.05 \cdot 10^{-58}:\\ \;\;\;\;\frac{b}{c} - \frac{\frac{d \cdot a}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\mathsf{hypot}\left(c, d\right) \cdot \left(\mathsf{hypot}\left(c, d\right) \cdot \frac{1}{c}\right)} - \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.48e+141)
   (- (/ (/ b d) (/ d c)) (/ a d))
   (if (<= d -1.15e-105)
     (- (/ b (/ (pow (hypot c d) 2.0) c)) (* d (* a (pow (hypot c d) -2.0))))
     (if (<= d 1.05e-58)
       (- (/ b c) (/ (/ (* d a) (hypot c d)) (hypot c d)))
       (-
        (/ b (* (hypot c d) (* (hypot c d) (/ 1.0 c))))
        (/ a (hypot c d)))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.48e+141) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -1.15e-105) {
		tmp = (b / (pow(hypot(c, d), 2.0) / c)) - (d * (a * pow(hypot(c, d), -2.0)));
	} else if (d <= 1.05e-58) {
		tmp = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	} else {
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - (a / hypot(c, d));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.48e+141) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -1.15e-105) {
		tmp = (b / (Math.pow(Math.hypot(c, d), 2.0) / c)) - (d * (a * Math.pow(Math.hypot(c, d), -2.0)));
	} else if (d <= 1.05e-58) {
		tmp = (b / c) - (((d * a) / Math.hypot(c, d)) / Math.hypot(c, d));
	} else {
		tmp = (b / (Math.hypot(c, d) * (Math.hypot(c, d) * (1.0 / c)))) - (a / Math.hypot(c, d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.48e+141:
		tmp = ((b / d) / (d / c)) - (a / d)
	elif d <= -1.15e-105:
		tmp = (b / (math.pow(math.hypot(c, d), 2.0) / c)) - (d * (a * math.pow(math.hypot(c, d), -2.0)))
	elif d <= 1.05e-58:
		tmp = (b / c) - (((d * a) / math.hypot(c, d)) / math.hypot(c, d))
	else:
		tmp = (b / (math.hypot(c, d) * (math.hypot(c, d) * (1.0 / c)))) - (a / math.hypot(c, d))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.48e+141)
		tmp = Float64(Float64(Float64(b / d) / Float64(d / c)) - Float64(a / d));
	elseif (d <= -1.15e-105)
		tmp = Float64(Float64(b / Float64((hypot(c, d) ^ 2.0) / c)) - Float64(d * Float64(a * (hypot(c, d) ^ -2.0))));
	elseif (d <= 1.05e-58)
		tmp = Float64(Float64(b / c) - Float64(Float64(Float64(d * a) / hypot(c, d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(b / Float64(hypot(c, d) * Float64(hypot(c, d) * Float64(1.0 / c)))) - Float64(a / hypot(c, d)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -1.48e+141)
		tmp = ((b / d) / (d / c)) - (a / d);
	elseif (d <= -1.15e-105)
		tmp = (b / ((hypot(c, d) ^ 2.0) / c)) - (d * (a * (hypot(c, d) ^ -2.0)));
	elseif (d <= 1.05e-58)
		tmp = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	else
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - (a / hypot(c, d));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.48e+141], N[(N[(N[(b / d), $MachinePrecision] / N[(d / c), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -1.15e-105], N[(N[(b / N[(N[Power[N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision], 2.0], $MachinePrecision] / c), $MachinePrecision]), $MachinePrecision] - N[(d * N[(a * N[Power[N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 1.05e-58], N[(N[(b / c), $MachinePrecision] - N[(N[(N[(d * a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 84.6% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := {\left(\mathsf{hypot}\left(c, d\right)\right)}^{2}\\ \mathbf{if}\;d \leq -7.8 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{b}{d}}{\frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -7 \cdot 10^{-108}:\\ \;\;\;\;\frac{b}{\frac{t_0}{c}} - d \cdot \frac{a}{t_0}\\ \mathbf{elif}\;d \leq 2.3 \cdot 10^{-55}:\\ \;\;\;\;\frac{b}{c} - \frac{\frac{d \cdot a}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\mathsf{hypot}\left(c, d\right) \cdot \left(\mathsf{hypot}\left(c, d\right) \cdot \frac{1}{c}\right)} - \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (pow (hypot c d) 2.0)))
   (if (<= d -7.8e+146)
     (- (/ (/ b d) (/ d c)) (/ a d))
     (if (<= d -7e-108)
       (- (/ b (/ t_0 c)) (* d (/ a t_0)))
       (if (<= d 2.3e-55)
         (- (/ b c) (/ (/ (* d a) (hypot c d)) (hypot c d)))
         (-
          (/ b (* (hypot c d) (* (hypot c d) (/ 1.0 c))))
          (/ a (hypot c d))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = pow(hypot(c, d), 2.0);
	double tmp;
	if (d <= -7.8e+146) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -7e-108) {
		tmp = (b / (t_0 / c)) - (d * (a / t_0));
	} else if (d <= 2.3e-55) {
		tmp = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	} else {
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - (a / hypot(c, d));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = Math.pow(Math.hypot(c, d), 2.0);
	double tmp;
	if (d <= -7.8e+146) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -7e-108) {
		tmp = (b / (t_0 / c)) - (d * (a / t_0));
	} else if (d <= 2.3e-55) {
		tmp = (b / c) - (((d * a) / Math.hypot(c, d)) / Math.hypot(c, d));
	} else {
		tmp = (b / (Math.hypot(c, d) * (Math.hypot(c, d) * (1.0 / c)))) - (a / Math.hypot(c, d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = math.pow(math.hypot(c, d), 2.0)
	tmp = 0
	if d <= -7.8e+146:
		tmp = ((b / d) / (d / c)) - (a / d)
	elif d <= -7e-108:
		tmp = (b / (t_0 / c)) - (d * (a / t_0))
	elif d <= 2.3e-55:
		tmp = (b / c) - (((d * a) / math.hypot(c, d)) / math.hypot(c, d))
	else:
		tmp = (b / (math.hypot(c, d) * (math.hypot(c, d) * (1.0 / c)))) - (a / math.hypot(c, d))
	return tmp

Julia

function code(a, b, c, d)
	t_0 = hypot(c, d) ^ 2.0
	tmp = 0.0
	if (d <= -7.8e+146)
		tmp = Float64(Float64(Float64(b / d) / Float64(d / c)) - Float64(a / d));
	elseif (d <= -7e-108)
		tmp = Float64(Float64(b / Float64(t_0 / c)) - Float64(d * Float64(a / t_0)));
	elseif (d <= 2.3e-55)
		tmp = Float64(Float64(b / c) - Float64(Float64(Float64(d * a) / hypot(c, d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(b / Float64(hypot(c, d) * Float64(hypot(c, d) * Float64(1.0 / c)))) - Float64(a / hypot(c, d)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = hypot(c, d) ^ 2.0;
	tmp = 0.0;
	if (d <= -7.8e+146)
		tmp = ((b / d) / (d / c)) - (a / d);
	elseif (d <= -7e-108)
		tmp = (b / (t_0 / c)) - (d * (a / t_0));
	elseif (d <= 2.3e-55)
		tmp = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	else
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - (a / hypot(c, d));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[Power[N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision], 2.0], $MachinePrecision]}, If[LessEqual[d, -7.8e+146], N[(N[(N[(b / d), $MachinePrecision] / N[(d / c), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -7e-108], N[(N[(b / N[(t$95$0 / c), $MachinePrecision]), $MachinePrecision] - N[(d * N[(a / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 2.3e-55], N[(N[(b / c), $MachinePrecision] - N[(N[(N[(d * a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 82.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.25 \cdot 10^{+19}:\\ \;\;\;\;\frac{c \cdot \frac{b}{d} - a}{d}\\ \mathbf{elif}\;d \leq 1.22 \cdot 10^{-58}:\\ \;\;\;\;\frac{b}{c} - \frac{\frac{d \cdot a}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{\mathsf{hypot}\left(c, d\right) \cdot \left(\mathsf{hypot}\left(c, d\right) \cdot \frac{1}{c}\right)} - \frac{a}{\mathsf{hypot}\left(c, d\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.25e+19)
   (/ (- (* c (/ b d)) a) d)
   (if (<= d 1.22e-58)
     (- (/ b c) (/ (/ (* d a) (hypot c d)) (hypot c d)))
     (- (/ b (* (hypot c d) (* (hypot c d) (/ 1.0 c)))) (/ a (hypot c d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.25e+19) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 1.22e-58) {
		tmp = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	} else {
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - (a / hypot(c, d));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.25e+19) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 1.22e-58) {
		tmp = (b / c) - (((d * a) / Math.hypot(c, d)) / Math.hypot(c, d));
	} else {
		tmp = (b / (Math.hypot(c, d) * (Math.hypot(c, d) * (1.0 / c)))) - (a / Math.hypot(c, d));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.25e+19:
		tmp = ((c * (b / d)) - a) / d
	elif d <= 1.22e-58:
		tmp = (b / c) - (((d * a) / math.hypot(c, d)) / math.hypot(c, d))
	else:
		tmp = (b / (math.hypot(c, d) * (math.hypot(c, d) * (1.0 / c)))) - (a / math.hypot(c, d))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.25e+19)
		tmp = Float64(Float64(Float64(c * Float64(b / d)) - a) / d);
	elseif (d <= 1.22e-58)
		tmp = Float64(Float64(b / c) - Float64(Float64(Float64(d * a) / hypot(c, d)) / hypot(c, d)));
	else
		tmp = Float64(Float64(b / Float64(hypot(c, d) * Float64(hypot(c, d) * Float64(1.0 / c)))) - Float64(a / hypot(c, d)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -1.25e+19)
		tmp = ((c * (b / d)) - a) / d;
	elseif (d <= 1.22e-58)
		tmp = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	else
		tmp = (b / (hypot(c, d) * (hypot(c, d) * (1.0 / c)))) - (a / hypot(c, d));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.25e+19], N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 1.22e-58], N[(N[(b / c), $MachinePrecision] - N[(N[(N[(d * a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * N[(1.0 / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 81.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b}{c} - \frac{\frac{d \cdot a}{\mathsf{hypot}\left(c, d\right)}}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{if}\;d \leq -1.9 \cdot 10^{+18}:\\ \;\;\;\;\frac{c \cdot \frac{b}{d} - a}{d}\\ \mathbf{elif}\;d \leq 4.2 \cdot 10^{-73}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 4.8 \cdot 10^{+47}:\\ \;\;\;\;\frac{b \cdot c - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{elif}\;d \leq 8.6 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{\frac{b}{d}}{d} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (- (/ b c) (/ (/ (* d a) (hypot c d)) (hypot c d)))))
   (if (<= d -1.9e+18)
     (/ (- (* c (/ b d)) a) d)
     (if (<= d 4.2e-73)
       t_0
       (if (<= d 4.8e+47)
         (/ (- (* b c) (* d a)) (+ (* c c) (* d d)))
         (if (<= d 8.6e+65) t_0 (- (* c (/ (/ b d) d)) (/ a d))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	double tmp;
	if (d <= -1.9e+18) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 4.2e-73) {
		tmp = t_0;
	} else if (d <= 4.8e+47) {
		tmp = ((b * c) - (d * a)) / ((c * c) + (d * d));
	} else if (d <= 8.6e+65) {
		tmp = t_0;
	} else {
		tmp = (c * ((b / d) / d)) - (a / d);
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = (b / c) - (((d * a) / Math.hypot(c, d)) / Math.hypot(c, d));
	double tmp;
	if (d <= -1.9e+18) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 4.2e-73) {
		tmp = t_0;
	} else if (d <= 4.8e+47) {
		tmp = ((b * c) - (d * a)) / ((c * c) + (d * d));
	} else if (d <= 8.6e+65) {
		tmp = t_0;
	} else {
		tmp = (c * ((b / d) / d)) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = (b / c) - (((d * a) / math.hypot(c, d)) / math.hypot(c, d))
	tmp = 0
	if d <= -1.9e+18:
		tmp = ((c * (b / d)) - a) / d
	elif d <= 4.2e-73:
		tmp = t_0
	elif d <= 4.8e+47:
		tmp = ((b * c) - (d * a)) / ((c * c) + (d * d))
	elif d <= 8.6e+65:
		tmp = t_0
	else:
		tmp = (c * ((b / d) / d)) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(b / c) - Float64(Float64(Float64(d * a) / hypot(c, d)) / hypot(c, d)))
	tmp = 0.0
	if (d <= -1.9e+18)
		tmp = Float64(Float64(Float64(c * Float64(b / d)) - a) / d);
	elseif (d <= 4.2e-73)
		tmp = t_0;
	elseif (d <= 4.8e+47)
		tmp = Float64(Float64(Float64(b * c) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)));
	elseif (d <= 8.6e+65)
		tmp = t_0;
	else
		tmp = Float64(Float64(c * Float64(Float64(b / d) / d)) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = (b / c) - (((d * a) / hypot(c, d)) / hypot(c, d));
	tmp = 0.0;
	if (d <= -1.9e+18)
		tmp = ((c * (b / d)) - a) / d;
	elseif (d <= 4.2e-73)
		tmp = t_0;
	elseif (d <= 4.8e+47)
		tmp = ((b * c) - (d * a)) / ((c * c) + (d * d));
	elseif (d <= 8.6e+65)
		tmp = t_0;
	else
		tmp = (c * ((b / d) / d)) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(b / c), $MachinePrecision] - N[(N[(N[(d * a), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -1.9e+18], N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 4.2e-73], t$95$0, If[LessEqual[d, 4.8e+47], N[(N[(N[(b * c), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 8.6e+65], t$95$0, N[(N[(c * N[(N[(b / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 79.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;c \leq -9.2 \cdot 10^{+24}:\\ \;\;\;\;\frac{c}{\mathsf{hypot}\left(c, d\right)} \cdot \frac{b}{\mathsf{hypot}\left(c, d\right)}\\ \mathbf{elif}\;c \leq 1.35 \cdot 10^{-129}:\\ \;\;\;\;\frac{\frac{b \cdot c}{d}}{d} - \frac{a}{d}\\ \mathbf{elif}\;c \leq 9.2 \cdot 10^{+29}:\\ \;\;\;\;\frac{b \cdot c - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c} - d \cdot \frac{a}{{\left(\mathsf{hypot}\left(c, d\right)\right)}^{2}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= c -9.2e+24)
   (* (/ c (hypot c d)) (/ b (hypot c d)))
   (if (<= c 1.35e-129)
     (- (/ (/ (* b c) d) d) (/ a d))
     (if (<= c 9.2e+29)
       (/ (- (* b c) (* d a)) (+ (* c c) (* d d)))
       (- (/ b c) (* d (/ a (pow (hypot c d) 2.0))))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -9.2e+24) {
		tmp = (c / hypot(c, d)) * (b / hypot(c, d));
	} else if (c <= 1.35e-129) {
		tmp = (((b * c) / d) / d) - (a / d);
	} else if (c <= 9.2e+29) {
		tmp = ((b * c) - (d * a)) / ((c * c) + (d * d));
	} else {
		tmp = (b / c) - (d * (a / pow(hypot(c, d), 2.0)));
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (c <= -9.2e+24) {
		tmp = (c / Math.hypot(c, d)) * (b / Math.hypot(c, d));
	} else if (c <= 1.35e-129) {
		tmp = (((b * c) / d) / d) - (a / d);
	} else if (c <= 9.2e+29) {
		tmp = ((b * c) - (d * a)) / ((c * c) + (d * d));
	} else {
		tmp = (b / c) - (d * (a / Math.pow(Math.hypot(c, d), 2.0)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if c <= -9.2e+24:
		tmp = (c / math.hypot(c, d)) * (b / math.hypot(c, d))
	elif c <= 1.35e-129:
		tmp = (((b * c) / d) / d) - (a / d)
	elif c <= 9.2e+29:
		tmp = ((b * c) - (d * a)) / ((c * c) + (d * d))
	else:
		tmp = (b / c) - (d * (a / math.pow(math.hypot(c, d), 2.0)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (c <= -9.2e+24)
		tmp = Float64(Float64(c / hypot(c, d)) * Float64(b / hypot(c, d)));
	elseif (c <= 1.35e-129)
		tmp = Float64(Float64(Float64(Float64(b * c) / d) / d) - Float64(a / d));
	elseif (c <= 9.2e+29)
		tmp = Float64(Float64(Float64(b * c) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = Float64(Float64(b / c) - Float64(d * Float64(a / (hypot(c, d) ^ 2.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (c <= -9.2e+24)
		tmp = (c / hypot(c, d)) * (b / hypot(c, d));
	elseif (c <= 1.35e-129)
		tmp = (((b * c) / d) / d) - (a / d);
	elseif (c <= 9.2e+29)
		tmp = ((b * c) - (d * a)) / ((c * c) + (d * d));
	else
		tmp = (b / c) - (d * (a / (hypot(c, d) ^ 2.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[c, -9.2e+24], N[(N[(c / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision] * N[(b / N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 1.35e-129], N[(N[(N[(N[(b * c), $MachinePrecision] / d), $MachinePrecision] / d), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[c, 9.2e+29], N[(N[(N[(b * c), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(b / c), $MachinePrecision] - N[(d * N[(a / N[Power[N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 77.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b \cdot c - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{if}\;d \leq -2 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{b}{d}}{\frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -3.7 \cdot 10^{-97}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 1.9 \cdot 10^{-75}:\\ \;\;\;\;\frac{-b}{\mathsf{hypot}\left(c, d\right) \cdot \left(-\frac{\mathsf{hypot}\left(c, d\right)}{c}\right)}\\ \mathbf{elif}\;d \leq 8 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{1}{d \cdot \frac{d}{b}} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (* b c) (* d a)) (+ (* c c) (* d d)))))
   (if (<= d -2e+130)
     (- (/ (/ b d) (/ d c)) (/ a d))
     (if (<= d -3.7e-97)
       t_0
       (if (<= d 1.9e-75)
         (/ (- b) (* (hypot c d) (- (/ (hypot c d) c))))
         (if (<= d 8e+32) t_0 (- (* c (/ 1.0 (* d (/ d b)))) (/ a d))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -2e+130) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -3.7e-97) {
		tmp = t_0;
	} else if (d <= 1.9e-75) {
		tmp = -b / (hypot(c, d) * -(hypot(c, d) / c));
	} else if (d <= 8e+32) {
		tmp = t_0;
	} else {
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	}
	return tmp;
}

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -2e+130) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -3.7e-97) {
		tmp = t_0;
	} else if (d <= 1.9e-75) {
		tmp = -b / (Math.hypot(c, d) * -(Math.hypot(c, d) / c));
	} else if (d <= 8e+32) {
		tmp = t_0;
	} else {
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d))
	tmp = 0
	if d <= -2e+130:
		tmp = ((b / d) / (d / c)) - (a / d)
	elif d <= -3.7e-97:
		tmp = t_0
	elif d <= 1.9e-75:
		tmp = -b / (math.hypot(c, d) * -(math.hypot(c, d) / c))
	elif d <= 8e+32:
		tmp = t_0
	else:
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(b * c) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (d <= -2e+130)
		tmp = Float64(Float64(Float64(b / d) / Float64(d / c)) - Float64(a / d));
	elseif (d <= -3.7e-97)
		tmp = t_0;
	elseif (d <= 1.9e-75)
		tmp = Float64(Float64(-b) / Float64(hypot(c, d) * Float64(-Float64(hypot(c, d) / c))));
	elseif (d <= 8e+32)
		tmp = t_0;
	else
		tmp = Float64(Float64(c * Float64(1.0 / Float64(d * Float64(d / b)))) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (d <= -2e+130)
		tmp = ((b / d) / (d / c)) - (a / d);
	elseif (d <= -3.7e-97)
		tmp = t_0;
	elseif (d <= 1.9e-75)
		tmp = -b / (hypot(c, d) * -(hypot(c, d) / c));
	elseif (d <= 8e+32)
		tmp = t_0;
	else
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(b * c), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -2e+130], N[(N[(N[(b / d), $MachinePrecision] / N[(d / c), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -3.7e-97], t$95$0, If[LessEqual[d, 1.9e-75], N[((-b) / N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] * (-N[(N[Sqrt[c ^ 2 + d ^ 2], $MachinePrecision] / c), $MachinePrecision])), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 8e+32], t$95$0, N[(N[(c * N[(1.0 / N[(d * N[(d / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 79.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b \cdot c - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{if}\;d \leq -4.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{\frac{b}{d}}{\frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -8.2 \cdot 10^{-100}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 5.2 \cdot 10^{-106}:\\ \;\;\;\;\frac{b}{c} - \frac{a}{\frac{{c}^{2}}{d}}\\ \mathbf{elif}\;d \leq 2.65 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{1}{d \cdot \frac{d}{b}} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (* b c) (* d a)) (+ (* c c) (* d d)))))
   (if (<= d -4.5e+130)
     (- (/ (/ b d) (/ d c)) (/ a d))
     (if (<= d -8.2e-100)
       t_0
       (if (<= d 5.2e-106)
         (- (/ b c) (/ a (/ (pow c 2.0) d)))
         (if (<= d 2.65e+32) t_0 (- (* c (/ 1.0 (* d (/ d b)))) (/ a d))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -4.5e+130) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -8.2e-100) {
		tmp = t_0;
	} else if (d <= 5.2e-106) {
		tmp = (b / c) - (a / (pow(c, 2.0) / d));
	} else if (d <= 2.65e+32) {
		tmp = t_0;
	} else {
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d))
    if (d <= (-4.5d+130)) then
        tmp = ((b / d) / (d / c)) - (a / d)
    else if (d <= (-8.2d-100)) then
        tmp = t_0
    else if (d <= 5.2d-106) then
        tmp = (b / c) - (a / ((c ** 2.0d0) / d))
    else if (d <= 2.65d+32) then
        tmp = t_0
    else
        tmp = (c * (1.0d0 / (d * (d / b)))) - (a / d)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -4.5e+130) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -8.2e-100) {
		tmp = t_0;
	} else if (d <= 5.2e-106) {
		tmp = (b / c) - (a / (Math.pow(c, 2.0) / d));
	} else if (d <= 2.65e+32) {
		tmp = t_0;
	} else {
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d))
	tmp = 0
	if d <= -4.5e+130:
		tmp = ((b / d) / (d / c)) - (a / d)
	elif d <= -8.2e-100:
		tmp = t_0
	elif d <= 5.2e-106:
		tmp = (b / c) - (a / (math.pow(c, 2.0) / d))
	elif d <= 2.65e+32:
		tmp = t_0
	else:
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(b * c) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (d <= -4.5e+130)
		tmp = Float64(Float64(Float64(b / d) / Float64(d / c)) - Float64(a / d));
	elseif (d <= -8.2e-100)
		tmp = t_0;
	elseif (d <= 5.2e-106)
		tmp = Float64(Float64(b / c) - Float64(a / Float64((c ^ 2.0) / d)));
	elseif (d <= 2.65e+32)
		tmp = t_0;
	else
		tmp = Float64(Float64(c * Float64(1.0 / Float64(d * Float64(d / b)))) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (d <= -4.5e+130)
		tmp = ((b / d) / (d / c)) - (a / d);
	elseif (d <= -8.2e-100)
		tmp = t_0;
	elseif (d <= 5.2e-106)
		tmp = (b / c) - (a / ((c ^ 2.0) / d));
	elseif (d <= 2.65e+32)
		tmp = t_0;
	else
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(b * c), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -4.5e+130], N[(N[(N[(b / d), $MachinePrecision] / N[(d / c), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -8.2e-100], t$95$0, If[LessEqual[d, 5.2e-106], N[(N[(b / c), $MachinePrecision] - N[(a / N[(N[Power[c, 2.0], $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, 2.65e+32], t$95$0, N[(N[(c * N[(1.0 / N[(d * N[(d / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 77.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{b \cdot c - d \cdot a}{c \cdot c + d \cdot d}\\ \mathbf{if}\;d \leq -3.5 \cdot 10^{+129}:\\ \;\;\;\;\frac{\frac{b}{d}}{\frac{d}{c}} - \frac{a}{d}\\ \mathbf{elif}\;d \leq -8.6 \cdot 10^{-189}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;d \leq 4.6 \cdot 10^{-96}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 9.5 \cdot 10^{+32}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{1}{d \cdot \frac{d}{b}} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (let* ((t_0 (/ (- (* b c) (* d a)) (+ (* c c) (* d d)))))
   (if (<= d -3.5e+129)
     (- (/ (/ b d) (/ d c)) (/ a d))
     (if (<= d -8.6e-189)
       t_0
       (if (<= d 4.6e-96)
         (/ b c)
         (if (<= d 9.5e+32) t_0 (- (* c (/ 1.0 (* d (/ d b)))) (/ a d))))))))

C

double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -3.5e+129) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -8.6e-189) {
		tmp = t_0;
	} else if (d <= 4.6e-96) {
		tmp = b / c;
	} else if (d <= 9.5e+32) {
		tmp = t_0;
	} else {
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d))
    if (d <= (-3.5d+129)) then
        tmp = ((b / d) / (d / c)) - (a / d)
    else if (d <= (-8.6d-189)) then
        tmp = t_0
    else if (d <= 4.6d-96) then
        tmp = b / c
    else if (d <= 9.5d+32) then
        tmp = t_0
    else
        tmp = (c * (1.0d0 / (d * (d / b)))) - (a / d)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	double tmp;
	if (d <= -3.5e+129) {
		tmp = ((b / d) / (d / c)) - (a / d);
	} else if (d <= -8.6e-189) {
		tmp = t_0;
	} else if (d <= 4.6e-96) {
		tmp = b / c;
	} else if (d <= 9.5e+32) {
		tmp = t_0;
	} else {
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d))
	tmp = 0
	if d <= -3.5e+129:
		tmp = ((b / d) / (d / c)) - (a / d)
	elif d <= -8.6e-189:
		tmp = t_0
	elif d <= 4.6e-96:
		tmp = b / c
	elif d <= 9.5e+32:
		tmp = t_0
	else:
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	t_0 = Float64(Float64(Float64(b * c) - Float64(d * a)) / Float64(Float64(c * c) + Float64(d * d)))
	tmp = 0.0
	if (d <= -3.5e+129)
		tmp = Float64(Float64(Float64(b / d) / Float64(d / c)) - Float64(a / d));
	elseif (d <= -8.6e-189)
		tmp = t_0;
	elseif (d <= 4.6e-96)
		tmp = Float64(b / c);
	elseif (d <= 9.5e+32)
		tmp = t_0;
	else
		tmp = Float64(Float64(c * Float64(1.0 / Float64(d * Float64(d / b)))) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	t_0 = ((b * c) - (d * a)) / ((c * c) + (d * d));
	tmp = 0.0;
	if (d <= -3.5e+129)
		tmp = ((b / d) / (d / c)) - (a / d);
	elseif (d <= -8.6e-189)
		tmp = t_0;
	elseif (d <= 4.6e-96)
		tmp = b / c;
	elseif (d <= 9.5e+32)
		tmp = t_0;
	else
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := Block[{t$95$0 = N[(N[(N[(b * c), $MachinePrecision] - N[(d * a), $MachinePrecision]), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[d, -3.5e+129], N[(N[(N[(b / d), $MachinePrecision] / N[(d / c), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision], If[LessEqual[d, -8.6e-189], t$95$0, If[LessEqual[d, 4.6e-96], N[(b / c), $MachinePrecision], If[LessEqual[d, 9.5e+32], t$95$0, N[(N[(c * N[(1.0 / N[(d * N[(d / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 69.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{c \cdot \frac{b}{d} - a}{d}\\ \mathbf{elif}\;d \leq 6.2 \cdot 10^{-74}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{d \cdot \left(-a\right)}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{1}{d \cdot \frac{d}{b}} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -9.5e+17)
   (/ (- (* c (/ b d)) a) d)
   (if (<= d 6.2e-74)
     (/ b c)
     (if (<= d 2.8e-11)
       (/ (* d (- a)) (+ (* c c) (* d d)))
       (- (* c (/ 1.0 (* d (/ d b)))) (/ a d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -9.5e+17) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 6.2e-74) {
		tmp = b / c;
	} else if (d <= 2.8e-11) {
		tmp = (d * -a) / ((c * c) + (d * d));
	} else {
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (d <= (-9.5d+17)) then
        tmp = ((c * (b / d)) - a) / d
    else if (d <= 6.2d-74) then
        tmp = b / c
    else if (d <= 2.8d-11) then
        tmp = (d * -a) / ((c * c) + (d * d))
    else
        tmp = (c * (1.0d0 / (d * (d / b)))) - (a / d)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -9.5e+17) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 6.2e-74) {
		tmp = b / c;
	} else if (d <= 2.8e-11) {
		tmp = (d * -a) / ((c * c) + (d * d));
	} else {
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -9.5e+17:
		tmp = ((c * (b / d)) - a) / d
	elif d <= 6.2e-74:
		tmp = b / c
	elif d <= 2.8e-11:
		tmp = (d * -a) / ((c * c) + (d * d))
	else:
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -9.5e+17)
		tmp = Float64(Float64(Float64(c * Float64(b / d)) - a) / d);
	elseif (d <= 6.2e-74)
		tmp = Float64(b / c);
	elseif (d <= 2.8e-11)
		tmp = Float64(Float64(d * Float64(-a)) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = Float64(Float64(c * Float64(1.0 / Float64(d * Float64(d / b)))) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -9.5e+17)
		tmp = ((c * (b / d)) - a) / d;
	elseif (d <= 6.2e-74)
		tmp = b / c;
	elseif (d <= 2.8e-11)
		tmp = (d * -a) / ((c * c) + (d * d));
	else
		tmp = (c * (1.0 / (d * (d / b)))) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -9.5e+17], N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 6.2e-74], N[(b / c), $MachinePrecision], If[LessEqual[d, 2.8e-11], N[(N[(d * (-a)), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(1.0 / N[(d * N[(d / b), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 69.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -9.5 \cdot 10^{+17}:\\ \;\;\;\;\frac{c \cdot \frac{b}{d} - a}{d}\\ \mathbf{elif}\;d \leq 1.35 \cdot 10^{-73}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{elif}\;d \leq 2.8 \cdot 10^{-11}:\\ \;\;\;\;\frac{d \cdot \left(-a\right)}{c \cdot c + d \cdot d}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{\frac{b}{d}}{d} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -9.5e+17)
   (/ (- (* c (/ b d)) a) d)
   (if (<= d 1.35e-73)
     (/ b c)
     (if (<= d 2.8e-11)
       (/ (* d (- a)) (+ (* c c) (* d d)))
       (- (* c (/ (/ b d) d)) (/ a d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -9.5e+17) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 1.35e-73) {
		tmp = b / c;
	} else if (d <= 2.8e-11) {
		tmp = (d * -a) / ((c * c) + (d * d));
	} else {
		tmp = (c * ((b / d) / d)) - (a / d);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (d <= (-9.5d+17)) then
        tmp = ((c * (b / d)) - a) / d
    else if (d <= 1.35d-73) then
        tmp = b / c
    else if (d <= 2.8d-11) then
        tmp = (d * -a) / ((c * c) + (d * d))
    else
        tmp = (c * ((b / d) / d)) - (a / d)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -9.5e+17) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 1.35e-73) {
		tmp = b / c;
	} else if (d <= 2.8e-11) {
		tmp = (d * -a) / ((c * c) + (d * d));
	} else {
		tmp = (c * ((b / d) / d)) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -9.5e+17:
		tmp = ((c * (b / d)) - a) / d
	elif d <= 1.35e-73:
		tmp = b / c
	elif d <= 2.8e-11:
		tmp = (d * -a) / ((c * c) + (d * d))
	else:
		tmp = (c * ((b / d) / d)) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -9.5e+17)
		tmp = Float64(Float64(Float64(c * Float64(b / d)) - a) / d);
	elseif (d <= 1.35e-73)
		tmp = Float64(b / c);
	elseif (d <= 2.8e-11)
		tmp = Float64(Float64(d * Float64(-a)) / Float64(Float64(c * c) + Float64(d * d)));
	else
		tmp = Float64(Float64(c * Float64(Float64(b / d) / d)) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -9.5e+17)
		tmp = ((c * (b / d)) - a) / d;
	elseif (d <= 1.35e-73)
		tmp = b / c;
	elseif (d <= 2.8e-11)
		tmp = (d * -a) / ((c * c) + (d * d));
	else
		tmp = (c * ((b / d) / d)) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -9.5e+17], N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 1.35e-73], N[(b / c), $MachinePrecision], If[LessEqual[d, 2.8e-11], N[(N[(d * (-a)), $MachinePrecision] / N[(N[(c * c), $MachinePrecision] + N[(d * d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(c * N[(N[(b / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 14: 69.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.4 \cdot 10^{+18}:\\ \;\;\;\;\frac{c \cdot \frac{b}{d} - a}{d}\\ \mathbf{elif}\;d \leq 2.9 \cdot 10^{-11}:\\ \;\;\;\;\frac{b}{c}\\ \mathbf{else}:\\ \;\;\;\;c \cdot \frac{\frac{b}{d}}{d} - \frac{a}{d}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (<= d -1.4e+18)
   (/ (- (* c (/ b d)) a) d)
   (if (<= d 2.9e-11) (/ b c) (- (* c (/ (/ b d) d)) (/ a d)))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.4e+18) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 2.9e-11) {
		tmp = b / c;
	} else {
		tmp = (c * ((b / d) / d)) - (a / d);
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (d <= (-1.4d+18)) then
        tmp = ((c * (b / d)) - a) / d
    else if (d <= 2.9d-11) then
        tmp = b / c
    else
        tmp = (c * ((b / d) / d)) - (a / d)
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (d <= -1.4e+18) {
		tmp = ((c * (b / d)) - a) / d;
	} else if (d <= 2.9e-11) {
		tmp = b / c;
	} else {
		tmp = (c * ((b / d) / d)) - (a / d);
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if d <= -1.4e+18:
		tmp = ((c * (b / d)) - a) / d
	elif d <= 2.9e-11:
		tmp = b / c
	else:
		tmp = (c * ((b / d) / d)) - (a / d)
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (d <= -1.4e+18)
		tmp = Float64(Float64(Float64(c * Float64(b / d)) - a) / d);
	elseif (d <= 2.9e-11)
		tmp = Float64(b / c);
	else
		tmp = Float64(Float64(c * Float64(Float64(b / d) / d)) - Float64(a / d));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (d <= -1.4e+18)
		tmp = ((c * (b / d)) - a) / d;
	elseif (d <= 2.9e-11)
		tmp = b / c;
	else
		tmp = (c * ((b / d) / d)) - (a / d);
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[LessEqual[d, -1.4e+18], N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], If[LessEqual[d, 2.9e-11], N[(b / c), $MachinePrecision], N[(N[(c * N[(N[(b / d), $MachinePrecision] / d), $MachinePrecision]), $MachinePrecision] - N[(a / d), $MachinePrecision]), $MachinePrecision]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 15: 69.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -9.5 \cdot 10^{+17} \lor \neg \left(d \leq 2.7 \cdot 10^{-11}\right):\\ \;\;\;\;\frac{c \cdot \frac{b}{d} - a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -9.5e+17) (not (<= d 2.7e-11)))
   (/ (- (* c (/ b d)) a) d)
   (/ b c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -9.5e+17) || !(d <= 2.7e-11)) {
		tmp = ((c * (b / d)) - a) / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-9.5d+17)) .or. (.not. (d <= 2.7d-11))) then
        tmp = ((c * (b / d)) - a) / d
    else
        tmp = b / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -9.5e+17) || !(d <= 2.7e-11)) {
		tmp = ((c * (b / d)) - a) / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -9.5e+17) or not (d <= 2.7e-11):
		tmp = ((c * (b / d)) - a) / d
	else:
		tmp = b / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -9.5e+17) || !(d <= 2.7e-11))
		tmp = Float64(Float64(Float64(c * Float64(b / d)) - a) / d);
	else
		tmp = Float64(b / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -9.5e+17) || ~((d <= 2.7e-11)))
		tmp = ((c * (b / d)) - a) / d;
	else
		tmp = b / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -9.5e+17], N[Not[LessEqual[d, 2.7e-11]], $MachinePrecision]], N[(N[(N[(c * N[(b / d), $MachinePrecision]), $MachinePrecision] - a), $MachinePrecision] / d), $MachinePrecision], N[(b / c), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 16: 63.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;d \leq -1.1 \cdot 10^{+18} \lor \neg \left(d \leq 1.1 \cdot 10^{+50}\right):\\ \;\;\;\;\frac{-a}{d}\\ \mathbf{else}:\\ \;\;\;\;\frac{b}{c}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (or (<= d -1.1e+18) (not (<= d 1.1e+50))) (/ (- a) d) (/ b c)))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.1e+18) || !(d <= 1.1e+50)) {
		tmp = -a / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if ((d <= (-1.1d+18)) .or. (.not. (d <= 1.1d+50))) then
        tmp = -a / d
    else
        tmp = b / c
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if ((d <= -1.1e+18) || !(d <= 1.1e+50)) {
		tmp = -a / d;
	} else {
		tmp = b / c;
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if (d <= -1.1e+18) or not (d <= 1.1e+50):
		tmp = -a / d
	else:
		tmp = b / c
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if ((d <= -1.1e+18) || !(d <= 1.1e+50))
		tmp = Float64(Float64(-a) / d);
	else
		tmp = Float64(b / c);
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if ((d <= -1.1e+18) || ~((d <= 1.1e+50)))
		tmp = -a / d;
	else
		tmp = b / c;
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Or[LessEqual[d, -1.1e+18], N[Not[LessEqual[d, 1.1e+50]], $MachinePrecision]], N[((-a) / d), $MachinePrecision], N[(b / c), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 17: 42.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ \frac{b}{c} \end{array} \]

FPCore

(FPCore (a b c d) :precision binary64 (/ b c))

C

double code(double a, double b, double c, double d) {
	return b / c;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    code = b / c
end function

Java

public static double code(double a, double b, double c, double d) {
	return b / c;
}

Python

def code(a, b, c, d):
	return b / c

Julia

function code(a, b, c, d)
	return Float64(b / c)
end

MATLAB

function tmp = code(a, b, c, d)
	tmp = b / c;
end

Wolfram

code[a_, b_, c_, d_] := N[(b / c), $MachinePrecision]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Developer target: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left|d\right| < \left|c\right|:\\ \;\;\;\;\frac{b - a \cdot \frac{d}{c}}{c + d \cdot \frac{d}{c}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(-a\right) + b \cdot \frac{c}{d}}{d + c \cdot \frac{c}{d}}\\ \end{array} \end{array} \]

FPCore

(FPCore (a b c d)
 :precision binary64
 (if (< (fabs d) (fabs c))
   (/ (- b (* a (/ d c))) (+ c (* d (/ d c))))
   (/ (+ (- a) (* b (/ c d))) (+ d (* c (/ c d))))))

C

double code(double a, double b, double c, double d) {
	double tmp;
	if (fabs(d) < fabs(c)) {
		tmp = (b - (a * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (-a + (b * (c / d))) / (d + (c * (c / d)));
	}
	return tmp;
}

Fortran

real(8) function code(a, b, c, d)
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8), intent (in) :: c
    real(8), intent (in) :: d
    real(8) :: tmp
    if (abs(d) < abs(c)) then
        tmp = (b - (a * (d / c))) / (c + (d * (d / c)))
    else
        tmp = (-a + (b * (c / d))) / (d + (c * (c / d)))
    end if
    code = tmp
end function

Java

public static double code(double a, double b, double c, double d) {
	double tmp;
	if (Math.abs(d) < Math.abs(c)) {
		tmp = (b - (a * (d / c))) / (c + (d * (d / c)));
	} else {
		tmp = (-a + (b * (c / d))) / (d + (c * (c / d)));
	}
	return tmp;
}

Python

def code(a, b, c, d):
	tmp = 0
	if math.fabs(d) < math.fabs(c):
		tmp = (b - (a * (d / c))) / (c + (d * (d / c)))
	else:
		tmp = (-a + (b * (c / d))) / (d + (c * (c / d)))
	return tmp

Julia

function code(a, b, c, d)
	tmp = 0.0
	if (abs(d) < abs(c))
		tmp = Float64(Float64(b - Float64(a * Float64(d / c))) / Float64(c + Float64(d * Float64(d / c))));
	else
		tmp = Float64(Float64(Float64(-a) + Float64(b * Float64(c / d))) / Float64(d + Float64(c * Float64(c / d))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(a, b, c, d)
	tmp = 0.0;
	if (abs(d) < abs(c))
		tmp = (b - (a * (d / c))) / (c + (d * (d / c)));
	else
		tmp = (-a + (b * (c / d))) / (d + (c * (c / d)));
	end
	tmp_2 = tmp;
end

Wolfram

code[a_, b_, c_, d_] := If[Less[N[Abs[d], $MachinePrecision], N[Abs[c], $MachinePrecision]], N[(N[(b - N[(a * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(c + N[(d * N[(d / c), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[((-a) + N[(b * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(d + N[(c * N[(c / d), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2023343 
(FPCore (a b c d)
  :name "Complex division, imag part"
  :precision binary64

  :herbie-target
  (if (< (fabs d) (fabs c)) (/ (- b (* a (/ d c))) (+ c (* d (/ d c)))) (/ (+ (- a) (* b (/ c d))) (+ d (* c (/ c d)))))

  (/ (- (* b c) (* a d)) (+ (* c c) (* d d))))